Chapter 2: Modulation - Universiti Malaysia Pahangee.ump.edu.my/hazlina/teaching_PCOM/Chapter2 Modulation and...•This process is known as “ Demodulation ... Example: Pulse Amplitude

9/18/2016 Nurul/DEE 3413/Modulation 1

Chapter 2:

Modulation


Communication System Chart

Communication

System

Continuous Wave Digital Wave

Amplitude

Modulation

(AM)

Pulse

Modulation

(PM)

Angle

Modulation

Frequency

Modulation

(FM)

Analogue Pulse

Modulation

Digital Pulse

Modulation


What is modulation?

“Modulation is defined as the process of modifying a carrier

wave (radio wave) systematically by the modulating signal

(audio)”

This process makes the signal suitable for the transmission and

compatible with the channel. The resultant signal is called the

modulated signal

In the other words, it is the process of changing/varying one of

the parameters of the carrier wave by the modulating signal

Introduction


Modulation is operation performed at the transmitter to achieve efficient and reliable information transmission

For analogue modulation, it is frequency translation method caused by changing the appropriate quantity in a carrier signal

It involves two waveforms:

A modulating signal/baseband signal – represents the message

A carrier signal – depends on type of modulation

Introduction


Introduction

Analogue modulations - frequency translation

methods caused by changing the appropriate

quantity in a carrier signal.

MODULATION Modulated

signal

Carrier

Baseband

signal


Introduction


•Once this information is received, the low frequency information

must be removed from the high frequency carrier.

•This process is known as “ Demodulation”.

Introduction


Types of Modulation

Three main type of modulations:

Analog Modulation

Amplitude modulation

Example: Double sideband with carrier (DSB-WC), Double sideband suppressed carrier (DSB-SC), Single sideband suppressed carrier (SSB-SC), Vestigial sideband (VSB)

Angle modulation (frequency modulation & phase modulation)

Example: Narrow band frequency modulation (NBFM), Wideband frequency modulation (WBFM), Narrowband phase modulation (NBPM), Wideband phase modulation (NBPM)


Types of Modulation

Pulse Modulation

Carrier is a train of pulses

Example: Pulse Amplitude Modulation (PAM), Pulse width modulation (PWM) , Pulse Position Modulation (PPM)

Digital Modulation

Modulating signal is analog Example: Pulse Code Modulation (PCM), Delta Modulation

(DM), Adaptive Delta Modulation (ADM), Differential Pulse Code Modulation (DPCM), Adaptive Differential Pulse Code Modulation (ADPCM) etc.

Modulating signal is digital (binary modulation) Example: Amplitude shift keying (ASK), frequency Shift Keying

(FSK), Phase Shift Keying (PSK) etc.


Summary of Modulation Techniques

v(t) = V sin )2( ftASK FSK PSK

Digital Modulation

AM FM PM

Analogue Modulation

Volt Hertz Radians


•Changing of the amplitude produces

Amplitude Modulation signal

•Changing of the frequency produces

Frequency Modulation signal

•Changing of the phase produces

Phase Modulation signal

Types of Modulation


Modulation 1

Analogue Modulation

Amplitude Modulation (13-60)



Communication

System


Amplitude

Modulation

(AM)

Pulse

Modulation

(PM)

Angle

Modulation

Frequency

Modulation

(FM)

Analogue Pulse

Modulation

Digital Pulse

Modulation


Amplitude Modulation

Various forms of Amplitude Modulation

• Conventional Amplitude Modulation (Alternatively known as Full AM or Double Sideband Large carrier modulation (DSBLC) /Double Sideband Full Carrier (DSBFC)

• Double Sideband Suppressed carrier (DSBSC) modulation

• Single Sideband (SSB) modulation

• Vestigial Sideband (VSB) modulation


Amplitude Modulation ~ DSBFC (Full AM)

“Amplitude Modulation is the process of changing the amplitude of the radio frequency (RF) carrier wave by the amplitude variations of modulating signal”

The carrier amplitude varied linearly by the modulating signal which usually consist of a range of a audio frequencies. The frequency of the carrier is not affected

Application of AM - Radio broadcasting, TV pictures

(video), facsimile transmission

Frequency range for AM - 535 kHz – 1600 kHz

Bandwidth - 10 kHz


In amplitude modulation, the amplitude of the carrier varies

proportional to the instantaneous magnitude of modulating signal

Assuming

Modulating signal : vm(t) = Vm cos wmt

carrier signal : vc(t) = Vc cos wct

AMPLITUDE

MODULATION

modulating

Signal

vm(t)

Modulated

Signal

Carrier wave

Vc cos wct

)cos()cos()( ttVVtv cmmcAM



ccccc f2 where)tcos(V)t(v

tVtv mmm cos)(

Carrier signal

Modulating signal ccccc f2 where)tcos(V)t(v

vam




0 5 10 15 20 25 30 35 40 45-1.5

-1

-0.5

0

0.5

1

1.5

maxVminV

V envelope vm

Vc max

maxVminV

vc instantaneous

V modulated signal vam

V envelope =

Vc + vm

vam = amplitude - V envelope

frequency - carrier


ccccc f2 where)tcos(V)t(v

tVtv mmm cos)(

Carrier signal

Modulating signal



The amplitude-modulated wave can then be expressed as

)cos()()cos()( ttvtVtv cmccAM

)cos()()( ttvVtv cmcAM

)cos()cos()( ttVVtv cmmcAM

tV

VtVtv m

c

mccAM cos1)cos()(

tmtVtv maccAM cos1)cos()(



where notation m is termed the modulation index. It is

simply a measurement for the degree of modulation and

bears the relationship of Vm to Vc

c

ma

V

Vm

Therefore the full AM signal may be written as

tmtVtv maccAM cos(1)cos()(



)]cos()[cos(2/1coscos BABABA

tVm

tVm

tVtv mcca

mcca

ccAm )cos(2

)cos(2

)(cos)(

Carrier component

Upper sideband component

Lower sideband component

Using

So, with the modulating process, the original modulating signal is transferred to a different frequency spectrum with a higher value frequency



The frequency spectrum of AM waveform contains 3 parts:

• A component at the carrier frequency fc

• An upper sideband (USB), whose highest frequency component is at fc+fm

• A lower sideband (LSB), whose highest frequency component is at fc-fm

• The bandwidth of the modulated waveform is twice the information signal bandwidth.

# sideband is a component above and below centre frequency # Every sideband contains all the original message, but not the carrier



DSBFC Frequency Spectrum

With single frequency fm

B = Maximum freq. - minimum freq.

= (fc+fm)-(fc-fm) = fc+fm-fc+fm = 2fm

fC fc+fm fc-fm

2fm

cV

2

ca

Vm

2

ca

Vm

freq



If fm consists of a range frequencies f1 to f2, the component of the sidebands become:

Upper sideband (USB) range is from (fc+f1) to (fc+f2)

Lower sideband (LSB) range is from (fc-f2) to (fc-f1)

Bandwidth for this case, B = (fc+f2) - (fc-f2) = 2f2

AM spectrum when the modulating signal is a baseband signal from frequency f1 to f2

f1 f2 fc-f2 fc-f1 fc+f1 fc+f2

Amplitude,V Amplitude,V

Baseband signal lower sideband upper sideband

Modulated signal

freq freq



For example, if voice signal with the band of frequency of

0 – 4 kHz is transmitted using a carrier of 100 kHz, the

modulated signal consists of

Carrier signal with frequency of 100 kHz

upper side band with frequency of range of 100 – 104 kHz

lower side band with frequency of range 96 – 100 kHz

The bandwidth is 104 – 96 = 8 kHz



Modulation Index m (Coefficient of Modulation)

m is merely defined as a parameter, which determines the

amount of modulation.

What is the degree of modulation required to establish a

desirable AM communication link?

Answer is to maintain m<1.0 (m<100%).

This is important for successful retrieval of the original

transmitted information at the receiver end.


Modulation Index m


Modulation Index m


m must have a value between 0 and 1 to avoid over-modulation This modulation is known as double sideband with carrier

Modulation Index m


If the amplitude of the modulating signal is higher than the

carrier amplitude, which in turn implies the modulation index

. This will cause severe distortion to the

modulated signal.

%)100(0.1m

Modulation Index m


The ideal condition for amplitude modulation (AM) is when

m=1, which also means Vm=Vc.

This will give rise to the generation of the maximum

message signal output at the receiver without distortion.

Modulation Index m


If the modulating signal is pure, single-frequency sine

wave and the modulation process is symmetrical (i.e., the

positive and negative excursion of the envelope's

amplitude are equal), then percent modulation as follows:

Vm = ½ (Vmax – Vmin) and Vc = ½ (Vmax + Vmin)

Therefore, m = =

100xmin)VmaxV(2/1

min)VmaxV(2/1

100x

min)VmaxV(

min)VmaxV(

min)VmaxV(4

1

2

min)VmaxV(2/1

Modulation Index m


The peak change in the amplitude of the output wave (Vm) is the sum of the voltage from the upper and lower side frequencies. Therefore Since Vm = Vusf + Vlsf and Vusf = Vlsf , then Vusf = Vlsf = Vm/2 = Vusf = peak amplitude of the upper side frequency (volts)

Vlsf = peak amplitude of the lower side frequency (volts)

Modulation Index m


0 5 10 15 20 25 30 35 40 45-1.5

-1

-0.5

0

0.5

1

1.5

maxVminV

Vm

Vc

maxVminV

Modulation Index m


minmax

minmaxVV

VV

cVm

Vma

VmVcV

VmVcV

min

max

The modulation index can be determined by measuring the

actual values of the modulation voltage and the carrier voltage

and computing the ratio.

Modulation Index m


Trapezoid waveform can be obtained from by connecting the modulating signal to x-axis of an oscilloscope and modulated signal to y-axis of the oscilloscope

m = 0 m = 1 m > 1

a b

0< m < 1

Thus, m can be calculated as

babama

Modulation Index m


AM Power Distribution

tVm

tVm

tVtv mcca

mcca

ccAm )cos(2

)cos(2

)(cos)(

For a single frequency signal, average power for each component is (assume transmission impedance is R):


The total transmitted power is

the sum of the carrier power

and the power in the

sidebands.

21

2

ac

SBc

LSBUSBctotal

mP

PP

pPPP

Carrier power :

R

VP c

c2

2

Sideband power: 48

222

cacaLSBUSB

Pm

R

VmPP

2

2

caLSBUSBSB

PmPPP



2

2

caLSBUSBSB

PmPPP

The efficiency of the AM in term of power consumption is Thus, at optimum operation (m = 100%), only 33% of power is used to carry information From previous equation, total current flow in AM is

22

2

a

a

T

SB

m

m

P

P



Generation and Detection of Full AM

Both generation and detection require multiplication to be performed.

The multiplication is achieved by using a network with a nonlinear characteristic.

Nonlinear networks are not true multipliers because other components are produced and need to be filtered out.


Square-Law Modulator

Consists of a summer (summing the carrier and

modulating signal), nonlinearity (square-law) block and a

band pass filter (BPF) of bandwidth (2B) centered at fc to

extract the desired modulation products.


Square law of nonlinearity:

v2(t) = a1v1(t) + a2v12(t)

where, a1 and a2 are constants and v1 is the input voltage signal consist of the carrier plus the modulation signal

v1(t) = Sc(t) + Sm(t) = Vc cos(wct) + Sm(t)

v2(t) = a1Vc(1 + 2a2/a1 Sm(t)) cos(wct) + a1Sm(t) + a2Sm

2(t) + a2Ac2cos2wct

By letting a1 = 1 , a2 = ½ Ac

vo = Ac (1 + mcos(wmt)) cos(wct) ---------Full AM signal

Square-Law Modulator


Square-Law Detector

Although above is described as a modulator, it can also

be used as a demodulator provided that the BPF is

replaced by a low pass filter (LPF) with cutoff

frequency at fm (i.e.; bandwidth of B) and a local

carrier signal oscillator.


Envelope Detector

However, envelope detector is yet another full AM detector commonly employed to replace the square-law detector. Since it is more simple and highly effective device produces a waveform at its output that is proportional to the real envelope of its input;

i.e. the output of the detector simply follows the envelope of the input signal.


Make an initial assumption that the input (AM signal) is of fixed amplitude and ignore the present of the resistor R. Following this, the capacitor C charges to the peak positive voltage of the carrier. It capacitor) then holds this peak voltage, results the diode stop conducting. Suppose now that the input-carrier amplitude is made to increase. Again, the diode resumes conduction, and the capacitor charges to a new higher carrier peak. To ensure that the capacitor voltage vc to follow the carrier peaks when the carrier amplitude is decreasing, it is required to include the resistor R, so the capacitor C may discharge. In this case the capacitor voltage vc has the form shown in (AM waveform); i.e. the positive portion of the modulated signal envelope approximates the modulating information signal. An additional LPF might be needed to effectively smoothen out the saw tooth distortion of the envelope waveform shown in figure (AM waveform) after the envelope detector.

Envelope Detector - Operation


m for Complex Signal

As most of the signals are complex and can be represented by combination of various sine waves, m can be determined by

Thus, total power for this complex signal is

......2

3

2

2

2

1 mmmmm effa

]2

1[

2

eff

cT

mPP


The previous modulated signal (DSBFC) has two drawbacks; it waste power and bandwidth

Power sent as the carrier contains no information and each sideband carries the same information independently

The double sideband suppressed carrier (DSBSC) is introduced to eliminate carrier hence improve power efficiency

It is a technique where it is transmitting both the sidebands without the carrier (the carrier is being suppressed)

Amplitude Modulation ~

Double Sideband Suppress Carrier (DSBSC)


The equation, then is simplified to

fc-fm fc+fm

ttVV

ttVVtv mcmcmc

mcmcDSBSC )cos()cos(2

coscos)(

LSB USB

freq freq

Frequency spectrum of a DSBSC system

LSBUSBtotal pPP Total power in DSBSC

Although, the power is improved, the bandwidth remain unchanged,

that is BW = 2B = 2 fmax

Amplitude Modulation ~ DSBSC


The suppressed carrier is further improved by sending only one sideband

This not only uses less power but also only half of the bandwidth and it is called single sideband suppressed carrier (SSBSC)

There are two possible of SSBSC

the lower sideband VLSB = Vm cos (wc-wm)t

the upper sideband VUSB = Vm cos (wc+wm)t

Amplitude Modulation ~ DSBSC


As both DSB and standard AM waste a lot of power and

occupy large bandwidth, SSB is adopted

SSB is a process of transmitting one of the sidebands of the

standard AM by suppressing the carrier and one of the

sidebands (only transmits upper or lower sideband of AM)

Reduces bandwidth by factor of 2

Frequency spectrum of a SSB system

LSBUSBtotal pPP Total power in SSB

fc

LSB USB LSB

fc

USB

Amplitude Modulation ~ Single Sideband (SSB)


SSB Applications:

SSB is used in the systems which require minimum

bandwidth such as telephone multiplex system and it is

not used in broadcasting

Point to point communications at frequency below 30

MHz – mobile communications, military, navigation radio

etc where power saving is needed

Amplitude Modulation ~ Single Sideband (SSB)


VSB is a technique AM transmission where the carrier, one sideband and a part of the other sideband are transmitted

VSB application: VSB is mainly used in TV broadcasting for their video

transmissions. TV signal consists of: Audio signal – is transmitted by FM Video signal – is transmitted by VSB

Amplitude Modulation ~ Vestigial Sideband


A video signal consists of range of frequencies and maximum frequency is as high as 4.5Mhz. If it is transmitted using the conventional AM system, the required bandwidth is 9.0 Mhz (B=2fm). But according to the standardization, TV signal is limited to 6MHz only. So, to reduce to 6Mhz bandwidth, a part of the LSB is not transmitted. In this case SSB transmission is not applied as it is very difficult to suppress a sideband accurately at high frequency.



Carrier

for video

Audio

Signal

(FM) Upper sideband

Lower

Side

band

fc-1.25 fc fc+4.5 4.5 MHz

Carrier

for audio

Frequency spectrum of a Vestigial Sideband



Conclusion

Only sidebands contain the information

Lower and upper sideband are identical. Only one sideband is enough to recover the original signal

Carrier component does not contain any information but constitute 2/3 of the total power, at full modulation (ma=1)


Advantages and Disadvantages of AM

Advantages:

simple with proven reliability

low cost

Disadvantages:

wastage of power as most of the transmitted power are in the carrier component which does not contain information. When ma=1, 2/3 of the power is wasted

AM requires a bandwidth which is double to audio frequency

Noisy


AM Communication Chart

Continuous Wave

Amplitude

Modulation

(AM)

Phase

Modulation

(PM)

Angle

Modulation

Frequency

Modulation

(FM) DSBFC DSBSC Vestigial SSB


Examples

2.1 For an AM modulator with carrier frequency of 150 kHz and a modulating signal frequency of

10 kHz, determine the:

(i) Freq for the upper and lower sideband

(ii) bandwidth

Sketch the output frequency spectrum

Solution:

i) The lower and upper side band frequency

fLSB = fc – fm = 150 kHz – 10 kHz = 140 kHz fUSB = fc + fm = 150 kHz + 10 kHz =

160 kHz

i) Bandwidth

B = 2fm = 2 (10) kHz = 20 kHz

The output frequency spectrum is as shown:

Vc

(maVc)/2 (maVc)/2

140 160 150 f (kHz)

B = 20 kHz


Examples

2.2 For an AM wave with a peak unmodulated carrier voltage Vc = 20 V, a load resistance RL =

20 ohm and a modulation index ma = 0.2, determine :

(i) Power contained in the carrier and the upper and lower sidebands

(ii) Total sideband power

(iii) Total power of the modulated power

Solution:

(i) The carrier power is

(i) The total sideband

(i) The total power in the modulated wave:

WR

cV

cP 10)20(2

220

2

2

wc

Pa

m

R

cV

am

USBPLSBP 1.04

)10(2)2.0(

4

2

8

22

wc

pa

m

SBP 2.02

)10(2)2.0(

2

2

wLSBPUSBPSBP 2.01.01.0

OR

Wa

m

cPTP 2.10]

2

2)2.0(1[10]

2

2

1[ wSBPcPTP 2.102.010

OR


Modulation 2

Analogue Modulation Angle Modulation (62-112)



Communication

System


Amplitude

Modulation

(AM)

Pulse

Modulation

(PM)

Angle

Modulation

Frequency

Modulation

(FM)

Analogue Pulse

Modulation

Digital Pulse

Modulation


Types of Modulation Process


Types of Modulation Process


Analog

Modulation


1. FREQUENCY MODULATION (FM)

2. PHASE MODULATION (PM).

Types of angle modulation


FM Communication Chart

Continuous Wave

Amplitude

Modulation

(AM)

Pulse

Modulation

(PM)

Angle

Modulation

Frequency

Modulation



Angle Modulation

FM PM


FREQUENCY-MODULATION SYSTEM

Angle Modulation

In angle modulation, the amplitude of the modulated carrier

is held constant and either the phase or the time derivative

of the phase of the carrier is varied linearly with the

message signal vm(t).


Frequency Modulation

Introduction

As in Chapter 1, the need for modulation arises because the range of frequencies contained in a baseband signal is not, in general, the same as the range of frequencies which can be transmitted by the communications channel.

AM – amplitude modulation

medium wave (300 kHz to 3 MHz), short wave (3–30 MHz)

FM – frequency modulation

VHF (30 – 300 MHz )


Frequency Modulation (FM)

Introduction

FM is the process of varying the frequency of a carrier wave in proportion to a modulating signal.

The amplitude of the carrier is constant while its frequency and rate of changes varied by the modulating signal

FM modulator FM signal

Frequency modulated signal


The FM modulator receives two signals, the information signal from an external source and the carrier signal from a built in oscillator.

The modulator circuit combines the two signals producing a FM signal which is passed on to the transmission medium.


Introduction


Frequency Modulation Waveform

Point A, C and E are where the information signal is at 0V.

Point B is where the information signal is at the max. positive amplitude, point D is where the information signal is at the max. negative amplitude.

During the time from point A to B, the FM signal increases in freq.

to its max. value at point B. From point B to C, the FM signal freq.

decrease until reaching the freq. of the carrier signal which called

the center frequency.


• At point D is where the info signal has the max. negative amplitude.

• From point D to E, the FM signal increases until reaching the centre frequency.

Frequency Modulation Waveform



The important features about FM waveforms are:

i. The frequency varies

ii. The rate of change of carrier frequency changes is the

same as the frequency of the information signal

iii. The amount of carrier frequency changes is proportional to

the amplitude of the information signal

iv. The amplitude is constant


In FM, frequency changes with the change of the

amplitude of the information signal

FM Analysis

)cos()( tVtv ccc

tVtv mmm cos)(

Assume : Carrier signal:

Information signal:


Thus, the instantaneous modulated frequency,

tkV

tkv

mmc

mc

cos

)(

tfff

tV

kff

mc

mm

c

cos

cos2

k is constant proportionality

mf

m

Vkf

kVf

2

f = frequency deviation

fk = frequency deviation constant

(deviation sensitivity, Hz/V)

or

FM Analysis


Analysis of FM

twsinw

kVt

0gminAssu

twsinw

kVt

dttwcoskV

m

m

m

m

m

m

mm

ccF M

c

c

cF M

wcosV(t)v

w

w dt w

:as obtained is angle The

cosθV(t)v

The wave equation of the frequency modulation is:


)tsinmtcos(V)t(v mfccFM

m

m

m

mf

f

kVkVm

2

2mkV

f

m

ff

fm

where

FM modulation index

In the FM, the value of modulation index, mf can be any value

from zero to infinity 0 ≤ mf ≤ ∞

Analysis of FM


Carrier Frequency (fc)

As in AM, the carrier frequency in FM system must be higher than the information signal frequency.

FM radio : Uses carrier frequencies between 88 MHz and 108 MHz.

Television: Frequency range = 54 MHz – 806 MHz

No. of channels = 67 channels

Bandwidth = 6 MHz

VHF: 54 MHz – 216 MHz (channel 2 – channel 13)

UHF: 470 MHz – 806 MHz (channel 14 – channel 69)

608 MHz – 614 MHz ( Radio Astronomy )


Frequency deviation represents the maximum change of the instantaneous frequency of the FM signal from the carrier frequency.

A fundamental characteristic of an FM signal is that the frequency deviation is proportional to the amplitude of the modulating signal, Vm and independent of the modulating frequency, fm

Frequency Deviation

2mkV

f mVf or


fff c min

The highest frequency for FM wave is

fff c max

The minimum frequency for FM wave is

ffcs 2

The total change of the frequency from minimum frequency to the maximum frequency is called frequency carrier swing, fcs

Frequency Deviation


FM Frequency Spectrum

As obtained, the FM signal is

)sincos()( tmtVtv mfccFM

])tm

sinf

m[tc

sin)]tm

(sinf

m[tc

(cosc

V)t(FMv


Where Jn is a Bessel Function from first type, nth order

J0 - will give the amplitude of the carrier

Jn – will give the amplitude of the sidebands, with frequency )(

mn

c

....}5

J].....t)m

2c

cos(t)m

2c

[cos(2

J

]t)mc

cos(t)mc

[cos(1

Jtc

cos0

J{c

V)t(FMv

.....]}tm

3sin3

Jtm

sin1

J[tc

sin

.......]tm

4cos4

Jtm

2cos2

J0

J[tc

{cosc

V)t(FMv

By using mathematical expressions:

FM Frequency Spectrum


FM frequency spectrum

n nJ 12

npowercVnJcV )(222

From above equation, the FM waveform has a component at the carrier frequency and an unlimited series of frequency, above and below the carrier frequency as below figure. An important characteristic of Bessel function: or

n

n

n JJ )1()(

Relative amplitude for the sideband = Jn

Actual amplitude for the sideband = Jn x Vc


fc fc+fm fc+2fm fc+3fm fc-fm fc-2fm fc-3fm

|Jn|

J0

J1 J1

J2

J3 J3

J2

An FM frequency spectrum freq

FM frequency spectrum


Bessel Functions


TABLE OF BESSEL FUNCTIONS


• The first column gives the sideband number,

while the first row gives the modulation index.

• The remaining columns indicate the amplitudes

of the carrier and the various pairs of sidebands.

• Sidebands with relative magnitude of less than

0.001 have been eliminated.

Bessel Functions


Some of the carrier and sideband amplitudes have negative

signs. This means that the signal represented by that

amplitude is simply shifted in phase 180 (phase

inversion). As you can see, the spectrum of a FM signal

varies considerably in bandwidth depending upon the value

of the modulation index. The higher the modulation index,

the wider the bandwidth of the FM signal.

Bessel Functions


With the increase in the modulation index, the carrier

amplitude decreases while the amplitude of the various

sidebands increases. With some values of modulation index,

the carrier can disappear completely.

Bessel Functions


FM Bandwidth

• Theoretically, a FM signal contains an infinite number of side

frequencies so that the bandwidth required to transmit such

signal is infinite.

• However, since the values of Jn() become negligible for

sufficiently large n, the bandwidth of an angle-modulated

signal can be defined by considering only those terms that

contain significant power.


FM Bandwidth

(max)2. mnfWB

)(2 mffBW

Carson's rule is given by the expression

From Bessel table:

n = number of significant sideband

Carson’s rule is an approximation and gives transmission bandwidth that are slightly narrower than the bandwidths determined using the Bessel table.

actual bandwidth

approximate bandwidth


Examples

Calculate the bandwidth occupied by a FM signal with a modulation index of 2 and a highest modulating frequency of 2.5 kHz.

Example: Assuming a maximum frequency deviation of 5 kHz and a maximum modulating frequency of 2.5 kHz, the bandwidth would be

(max)2. mnfWB kHz

WB

30

5.262..

Solution:

Solution:

kHz

kHz

kHzkHzWB

15

5.72

)55.2(2..


Power in FM

R

cV

R

rmsV

FMP

2

22

In FM, the amplitude of the modulated signal is the same as the amplitude of the un-modulated carrier signal. Power of FM wave dissipated in a load, R is:

PFM = Pc

But the power in the carrier is distributed over the various FM sidebands that results from the modulation. This power is contained at the various frequency Spectrum components, in amounts determined by the mf and the corresponding Bessel Function


n

nn

JJc

PT

P

1

]222

0[

The average power of the modulated carrier (PT) must be equal to the average power of the un-modulated carrier

The FM average power is:

where Pc = carrier power n = number of pairs of significant sidebands

Power in FM


Narrow Band FM (NBFM)

1. Modulation index approximates to 1

2. The frequency modulation is between 5 kHz to 10khz

3. Bandwidth : 10 – 30kHz

4. The maximum modulating frequency : 3 kHz

5. NBFM is used for communication, in competition with

SSB, having its main applications in various form of

mobile communication (eg. Police, ambulances, etc)


Wide Band FM (NBFM)

1. Modulating frequency range from : 30 kHz – 15 kHz

2. The maximum frequency deviation frequency : 75 kHz

3. Modulation index is more than 1 (between 5 to 2500)

4. Bandwidth is approximately 15 times higher than the NBFM system

5. WBFM is used for broadcasting with or without stereo multiplex and for the sound accompanying TV transmission


Advantages of FM compared to AM

1. All the transmitted power in FM is useful, whereas in AM most of it in the transmitted carrier, which contains no useful information

2. FM has the advantages over the AM, of providing greater

protection from noise for the lowest modulating frequency

3. In FM, the transmitted amplitude is constant. This

characteristic has the advantages of significantly improving immunity to noise and interference


Disadvantages of FM compared to AM

1. Since the reception is limited to line of sight, the area of reception for FM is much smaller than AM

2. Equipments for the transmitter and receiver are

more expensive and complex 3. A much wider bandwidth is required by FM, up to

10 times larger than needed by AM. This is the most significant disadvantage of AM


Amplitude modulation has two drawbacks; that is serious

deficiencies in dynamic range and in noise immunity

For these reason, Frequency Modulation (FM) is

introduced. This is due FM is offering a wide dynamic

range which is suitable for high fidelity system such as in

FM stereo and can reduce the effect of noise

However, it require a wide bandwidth and a complex

system transceiver

Frequency Modulation


FM Waveform


PM Communication Chart

Continuous Wave

Amplitude

Modulation

(AM)

Pulse

Modulation

(PM)

Angle

Modulation

Frequency

Modulation



Phase Modulation (PM)

)cos( ccVv

Phase modulation is a system in which the phase of the carrier signal is varied by the information signal. The amplitude of the carrier is kept constant.

in the equation

is varied so that its magnitude is proportional to instantaneous amplitude of the modulating signal.

The phase


With PM, the maximum frequency deviation occurs during

the zero crossings of the modulating signal. That is, the

is proportional to the slope or first derivative of the

modulating signal.

f




)(cos)( tVtv ccc

)(cos)( tVtv mmm

tVtv ccPM )cos()(

PM equation:

tkVtv mmm cos)(

If Carrier signal

Modulating signal

The expression for PM wave is:

where



)coscos()( tkVtVtv mmccPM

pm mkV

Giving

where

= is the maximum value of phase change introduced by this particular modulation signal and is proportional to the maximum amplitude of the modulating signal



)coscos()( tmtVtv mpccPM

The range for

The value of

So, general equation for PM is

is

is called the modulation index for PM, which is denoted by mp



An example of a Phase Modulation Waveform


Comparison between PM & FM

mp KVm

Comparisons between PM and FM

1. The modulation index – is defined differently in each system

In FM its modulation index :

In PM its modulation index :

m

f

ff

m


2. In PM, the phase deviation is proportionally to the amplitude of the modulating signal and is independent of its frequency

3. In FM, the frequency deviation is proportionally to the amplitude of the modulating signal Vm as well as its frequency, fm

4. The main difference between PM and FM, is how the information signal will change the carrier signal.

Comparison between PM & FM



Communication

System


Amplitude

Modulation

(AM)

Pulse

Modulation

(PM)

Angle

Modulation

Frequency

Modulation

(FM)

Analogue Pulse

Modulation

Digital Pulse

Modulation

DSBFC DSBSC Vestigial SSB


Modulation 3

Digital Modulation

Analogue Pulse Modulation


Digital Modulation Chart

Communication

System


Amplitude

Modulation

(AM)

Pulse

Modulation

(PM)

Angle

Modulation

Frequency

Modulation

(FM)

Analogue Pulse

Modulation

Digital Pulse

Modulation

DSBFC DSBSC Vestigial SSB


Introduction

Pulse modulation includes many difference methods of converting information into pulse form for transferring pulses from a source to a destination.

Pulse modulation

Analog Pulse Modulation (APM)

Digital Pulse Modulation

Pulse modulation can be used to transmit analogue information, it is first converted into pulses by the process of sampling.


Sampling

Sampling is the process of taking a periodic sample of the waveform to be transmitted.

The sampling theorem (Nyquist theorem) is used to determined minimum sampling rate for any signal so that the signal will be correctly restored at the receiver.

Nyquist’s Sampling theorem:

mfsf 2

Where fs = sampling frequency

fm(max) = maximum frequency of the modulating signal


Sampling

Three basic condition of sampling process:

1. Sampling at fs=2fm(max)

fs 2fs 3fs fm(max) fs+fm(max) fs-fm(max)

V (volt)

f (Hz)


Sampling

2. Sampling at fs>2fm(max)

fs 2fs fm(max)

fs+fm(max)

fs-fm(max)

V (volt)

f (Hz)

Guardband

This sampling rate creates a guard band between fm(max) and the lowest frequency component fs-fm(max) of the sampling harmonics.


Sampling

3. Sampling at fs<2fm(max)

fs 2fs 3fs

fm(max) fs+fm(max)

fs-fm(max)

V (volt)

f (Hz)

Aliasing distortion

Aliasing occurs when a signal is sampled below its Nyquist rate

Aliasing: the distortion produced by the overlapping components from adjacent bands


Analogue Pulse Modulation Chart

Communication

System


Analogue Pulse

Modulation

Digital Pulse

Modulation

PAM PWM PPM


Analog Pulse Modulation (APM)

In APM, the carrier signal is in the form of pulse form, and the modulated signal is where one of the characteristics either (amplitude, width, or position) is changed according to the modulating/audio signal.

Three common techniques of APM:

Pulse amplitude modulation (PAM)

Pulse Width Modulation (PWM)

Pulse Position Modulation (PPM)


Waveforms for PAM, PWM and PPM

Modulating signal

carrier signal

PAM (dual polarity)

PWM

PPM


It is very similar to AM

The amplitude of a carrier signal is varied according to the amplitude of the modulating signal.

Two type PAM Dual- polarity PAM

Single -polarity PAM

Pulse Amplitude Modulation (PAM)


Pulse Width Modulation (PWM)

The technique of varying the width of the constant amplitude pulse proportional to the amplitude of the modulating signal.

PWM gives a better signal to noise performance than PAM


Pulse Position Modulation (PPM)

PPM is when the position of a constant width and constant amplitude pulse within prescribed time slot is varied according to the amplitude of the modulating signal.


Modulation 4

Digital Modulation

Digital Pulse Modulation


Digital Pulse Modulation Chart

Communication

System


Analogue Pulse

Modulation

Digital Pulse

Modulation

PAM PWM PPM


Digital Pulse Modulation (DPM)

Digital modulation is the process by which digital symbols are transformed into waveforms that are compatible with the characteristics of the channel

In DPM, a code is used to represent the amplitude of the samples that has been divided into various levels.


Digital system offers some advantages compared to analog system. There are:

Immune to channel noise and interference

Signals and messages can be coded for error detection and correction

Can carry a combination of traffics

It is easier and more efficient to multiplex several digital signal

More economical

Disadvantages:

Requires significantly more bandwidth

Requires precise time synchronization between the clocks in the transmitter and receivers

Digital Pulse Modulation (DPM)


Pulse Code Modulation (PCM)

PCM is a form of digital modulation

where groups of coded pulses are used

to represent the analog signal.

The analog signal is sampled and

converted to a fixed-length, serial binary

number for transmission.


A Block Diagram of a PCM system

(single channel)

Low

Pass

Filter

(LPF)

Sampler Quantizer Coder Digital

Modulator

Demodulator Decoder Expandor

Low

Pass

Filter

(LPF)

Digital signal

Analog

Signal

(i/p)

Analog

Signal

(o/p)

Transmitter

Receiver Digital signal

Channel


PCM

LPF (Pre alias filter) Is used to attenuate those high frequency components of the

signal that lie outside the band of interest

Sampler The filtered signal is sampled at a rate higher than the Nyquist

rate

Quantizer The conversion of an analog (continuous) sampler of the

signal into a digital (discrete) form is called quantizing process. It consists of prescribed numbers of discrete amplitude levels


Principles of PCM

Three main process in PCM transmission are

sampling, quantization and coding.

Sampling

Quantization

Encoding


Principles of PCM

Sampling

Process of taking samples of the analog signals at given interval of time. Only samples are being transmitted. If sufficient samples are sent and sampling theorem are met, the original signal can be constructed at the receiver

Quantization

Quantization is a process of assigning the analog signal samples to a pre-determined discrete levels.

The number of quantization levels, L depends on the number of bits per sample, n, used to code the signal where nL 2

mfsf 2


Principles of PCM

The magnitude of the minimum stepsize of the

quantization levels is called resolution,

The resolution depends on the maximum

voltage, Vmax and the minimum voltage, Vmin of

the information signal, where

v

1minmax

L

VVv


Principles of PCM

Minimum stepsize

(resolution)


Illustration of the quantization process

Principles of PCM


Quantization error or quantization noise is the

distortion introduced during the quantization process

when the modulating signal is not an exact value of

the quantization level.

The maximum quantization error,

Quantization error can be reduced by increasing the

number of quantization levels, but this will increase the

bandwidth required.

2

vQe

Principles of PCM


Principles of PCM

Encoding

In this process, the samples that has been divided into various levels is coded into respective codes where the samples that are the same number of level are coded into the same code

Ln 2logn = no of bit

L = quantization level


Example of binary number and 3-bit pulse code is shown

below:

Pulse waveform Binary number Quantized level

000

001 010

011

100

101

110

111

1 2

3

4

5

6

7

8

3-bit PCM code and waveform


PCM

Input signal

Sampling pulse

Sampled signal

Quantized signal

PCM signal

PCM code

Amplitude sampling point


PCM transmission bit rate and

bandwidth

Transmission bit rate (R) is the rate of information transmission (bits/s).

It depends on the sampling frequency and the number of bit per sample used to encode the signal.

Transmission bandwidth is equal to transmission bit rate

snfR (bits/sec)

snfhonbandwidtTransmissi (Hz)


MODEM

MODEM stands for MODulator and DEModulator.

Modem is an interface device consists of modulator and demodulator used in point-to-point data communication systems, through the public switching telephone networks (PSTN).


Functions of a modem

At the transmitter

It coverts digital data signal that are compatible to the transmission line characteristics. That is, it converts “1” and “0’s” of binary signal into FSK, QPSK or QAM signals. Also it gives voltage and current appropriate for interfacing with the telephone line

At the receiver

It converts analog signal back to digital data signals. That is, it converts FSK, QPSK or QAM signals into binary signal.

MODEM


MODEM

PC Modulator

Demodulator

Modulator

Demodulator PC PSTN

RS232

MODEM MODEM

RS232 Telephone line

A connection of 2 computer terminals using modems


Digital Modulation Technique

There are several digital modulation techniques used to modulate digital signal or data, depending on the application, the rate of transmission required, allocated bandwidth and cost.


Digital Pulse Modulation Chart

Communication

System


Analogue Pulse

Modulation

Digital Pulse

Modulation

PAM PWM PPM

ASK PSK FSK


In ASK, a carrier wave is switched ON and OFF by the input data or binary signals.

Amplitude shift keying (ASK)

ASK modulator

Data ASK signal

carrier

ASK generator


During a “mark” (binary 1), a carrier wave is transmitted and during a “space” (binary 0) the carrier is suppressed. Hence, it is also known as ON-OFF keying (OOK)

1 0 1 1

ASK Waveform

Amplitude shift keying (ASK)

Application of ASK

It is used in multichannel telegraph systems.

Simple ASK is no longer used in digital communication systems

due to noise problems.


FSK is a similar to standard FM except the modulating signal is a binary signal that varies between two discrete voltage levels rather than a continuously changing analog waveform

Two different carrier frequency are used and they are switched ON and OFF by the binary signals

“1” – ON “0”-OFF

Frequency Shift Keying (FSK)

Data

FSK generator

f1

f2

1 0 1 1

FSK signal


FSK

Application of FSK

FSK signaling schemes are used mainly for low-speed

digital data transmissions.

Advantages of FSK over ASK

ASK needs automatic gain control (AGC) to overcome

fading effect.

Relatively easy for FSK generation

The constant amplitude property for the carrier signal

does not waste power and does produce some

immunity to noise.


Phase Shift keying (PSK)

PSK is similar to Phase Modulation except the PSK input is a digital signal and there are limited number of output phase possible

The binary signal are used to switch the phase of carrier wave between two values which are normally 0º and 180º

ASK modulator

Data ASK signal

carrier PSK generator

•For binary “1”, the carrier has one phase. •For binary “0”, the carrier is reversed by 180º

1 0 1 1 m(t)


Phase Shift Keying

0

1

Bit

Time

1

2

1

4

0

6

0

3

1

5

1

7

1

8


Modulation 5

Multiplexing


Multiplexing System Chart

Communication

System


Analogue Pulse

Modulation

Digital Pulse

Modulation

PAM PWM PPM

Multiplexing

FDM TDM WDM


Multiplexing

Multiplex is a technique of transmission of information

from more than one source to more than one

destination on the same medium or facility.

Advantages:

Many signals can share an existing channel and make

better use of the channel capacity

allow several different signal to be clustered into a

single group, for easy handling and maintenance


Four simultaneous transmissions on a single circuit Computers Terminals

Multiplexer Multiplexer

Multiplexing


Multiplexing

Three common techniques of multiplexing:-

Frequency Division Multiplexing (FDM)

Time Division Multiplexing (TDM)

Wavelength Division Multiplexing (WDM)


Frequency division multiplexing (FDM)

Multiplexer Multiplexer

Channel 1

Channel 2

Channel 3

Source 1

Source 2

Source 3

2

3

1

In FDM, multiple sources that originally occupied the same

frequency spectrum are each converted to a different

frequency band and transmitted simultaneously over a

single wideband transmission system.

FDM is an analog multiplexing scheme, where the

information entering an FDM system is analog and it

remains analog throughout transmission


FDM

FDM system - transmitter FDM system - receiver


Time division multiplexing

Time division multiplexing (TDM) shares the circuit’s time allocation.

TDM is compatible with digital signals and makes good use of digital circuitry for these signal

Simplistically, TDM physically switches from originator to originator to share the time available, and the receiving unit does the same in synchronism.

Source 3

Multiplexer

Source 1

Source 2 2

3

1

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 Multiplexer


TDM

TDM system


Comparison between TDM and FDM

TDM: the individual channels are assigned to different

time slots but jumbled together in the frequency domain.

FDM : the individual channels are assigned to different

frequency slots but jumbled together in the time domain

TDM offers simpler instrumentation. In FDM, it requires

an analog subcarrier modulator, bandpass filter and

demodulator for every message signal


• There is no crosstalk or interference between adjacent channels in TDM as present in FDM. The interference in FDM is normally due to imperfect bandpass filtering and non-linear cross modulation

• In FDM, the bandwidth is used effectively

• The transmission medium of TDM is subjected to fading

Comparison between TDM and FDM


Wavelength Division Multiplexing (WDM)

WDM is a technology that enables many optical signals to be transmitted simultaneously by a single fiber cable

The basic principle behind WDM involves the transmission of multiples signals using several wavelengths without their interfering with one another.


WDM versus FDM

WDM is essentially the as FDM, where several signals are transmitted using different carriers, occupying non-overlapping bands of a frequency or wavelength spectrum

The most obvious difference between WDM and FDM is that optical frequencies (in THz) are much higher than radio frequencies (in MHz and GHz)


•FDM: channels all propagate at the same time and over

the same transmission medium and take the same

transmission path, but they occupy different bandwidths

•WDM: each channel propagates down the same

transmission medium at the same time, but each channel

occupies a different bandwidth (wavelength) and each

wavelength takes different transmission path.

WDM versus FDM



Communication

System


Amplitude

Modulation

(AM)

Angle

Modulation

Analogue Pulse

Modulation

Digital Pulse

Modulation

Multiplexing

FDM

TDM

WDM

DSBFC

DSBSC

Vestigial

SSB

PAM

PWM

PPM

ASK

PSK

FSK

FM

PM

Documents

Chapter 2: Modulation - Universiti Malaysia Pahangee.ump.edu.my/hazlina/teaching_PCOM/Chapter2 Modulation and...•This process is known as “ Demodulation ... Example: Pulse Amplitude